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HWS09_14 - P1112 Spring 2009 Homework#14 will not be...

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P1112 Spring 2009 Homework #14 will not be collected. Solutions posted Friday May 1, and some of the HW will be covered in section. Reading: 13.3 – 13.8 (you may skip 13.4 molecules) Problems: 1. Y&F 11.72 Lifting a bicycle wheel over a curb. 2. Y&F 13.55 Physical pendulum. 3. The position as a function of time t for a block of mass m oscillating on a horizontal ideal spring of spring constant k is x ( t ) = A cos( ω t ). (a) Write the oscillator's velocity v ( t ) and acceleration a ( t ) in the form C cos( ω t + φ ), with C > 0, and find the constants C and φ for each function. Your answers should be in terms of A, ω , and numerical constants. (b) Write the oscillator's kinetic energy K ( t ) and elastic potential energy U ( t ) as functions of time t that are linear in sine or cosine of t . Your answers should be in terms of A, ω , k, m, and numerical constants. [HINT: The following trig identities will be useful: sin 2 θ = (1 - cos2 θ )/2 and cos 2 θ = (1 + cos2 θ )/2.] (c) For two complete cycles of this oscillation, draw graphs showing the oscillator's position x ( t ), velocity v
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